Quadratic Equations (VCE SSCE Mathematical Methods): Quizzes

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Quadratic Equations
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What is the standard form of a quadratic equation?

ax2+bx+c=0ax^2 + bx + c = 0 where a0a \neq 0

What is the first step when solving a quadratic by factorisation?

Rearrange to standard form

What does the null factor theorem state?

If mn=0mn = 0, then m=0m = 0 or n=0n = 0

Why must one side equal zero for the null factor theorem to work?

Product of factors must equal zero

To factorise x2+11x+24x^2 + 11x + 24, find two numbers that do what?

Multiply to 24 and add to 11

If (x4)(x+3)=0(x - 4)(x + 3) = 0, what are the solutions?

x=4x = 4 or x=3x = -3

When the leading coefficient is not 1, what should you multiply it by?

The constant term

How can you verify your solutions are correct?

Substitute back into original equation

In real-world problems, what must lengths always be?

Positive

How many solutions does a quadratic equation typically have?

Two

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